There has been known a vehicular differential gear device operative to distribute a drive force, generated by a drive force source, to a left drive wheel and a right drive wheel while permitting a differential action between the left and right drive wheels. The differential gear device has a differential limiting apparatus that applies differential limiting torques to the left and right drive wheels, respectively, for limiting the differential action. A device disclosed in, for instance, Patent publication 1 corresponds to such vehicular differential limiting apparatus. The differential limiting apparatus distributes the drive force, delivered from the drive force source, to the left and right drive wheels while permitting the differential action between the left drive wheel and the right drive wheel. In this moment, the differential limiting torques, determined depending on a difference in rotation between the left and right drive wheels and an accelerator-opening, are applied to the left and right drive wheels depending on a vehicle condition such as a vehicle speed or the like. With such a structure, a freewheeling motion of a drive wheel placed in contact with a low μ-road i.e., low friction coefficient road is minimized. Thus, an output power of the drive force source is efficiently transferred to the drive wheels to render increased startup and acceleration response performance.    [Patent publication 1] Japanese Patent Publication 8-002277